3-7.  A rod has a diameter of 1.2 in, and its weight follows a random distribution . Determine the distribution of the maximum torsional stress in the rod at a section lacated at A due to the rod’s weight. Assume that only the the internal torque is taken into account.             

Solution:

Since we are only interested in the internal torque, from the free-body diagram, we have

;             

The polar moment of inertia of the cross section at A is . We have

Thus,  also follows a normal distribution, and

Thus,  follows a normal distribution .                                   Ans.